A differential quadrature analysis of vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses

Thin rectangular plates having two opposite edges simply supported, with those edges subjected to linearly varying in-plane stresses, and the other two edges clamped, are encountered in engineering practice. Recently, Leissa and Kang used the classical power series method and obtained the first known exact vibration and some buckling solutions. The classical plate theory based on the Kirchhoff hypothesis is employed in the analysis. The relatively wild character of the convergence is observed, however, and 20 or 30 more terms of the series are needed to obtain reasonably accurate results. The differential quadrature (DQ) method has proved an accurate and computationally efficient numerical method. Thus, the DQ method is used to study the vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses. Convergence study shows that DQ method with 15×15 or more non-uniform grid points can yield very accurate results for cases considered. Exactly the same, accurate results as of Leissa and Kang are easy to reproduce.